CN109241843A - Sky spectrum joint multiconstraint optimization nonnegative matrix solution mixing method - Google Patents
Sky spectrum joint multiconstraint optimization nonnegative matrix solution mixing method Download PDFInfo
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Abstract
The invention discloses a kind of empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing methods, the steps include: 1) EO-1 hyperion end member quantity survey；2) endmember spectra minimum range bound term is constructed；3) building abundance mixes norm sparsity constraints item；4) abundance figure gradient field group's sparsity constraints item is constructed；5) it establishes empty spectrum joint multiconstraint optimization nonnegative matrix solution and mixes model；6) alternating direction iteratively solves；7) the mixed gained end member of output solution and abundance figure.The present invention makes full use of high optical spectrum image end member spectrum and geometry centroid distance minimum, abundance sparsity and Piecewise Smooth characteristic, and the search space of end member and abundance solution is limited by multiple constraint, avoids Local Minimum, obtains optimal solution by iterative solution；Compared with traditional classical nonnegative matrix solution mixes model method, the present invention, which improves, understands mixed precision, enhances method to the robustness of noise, the unsupervised solution of EO-1 hyperion that can be widely applied to land resources, mineral products exploration and precision agriculture field is mixed.
Description
Technical field
The present invention relates to remote sensing hyperspectral data processing technology, specifically a kind of empty spectrum joint multiconstraint optimization nonnegative matrix
Solve mixing method.
Background technique
High-spectral data is widely used in military monitor, precisely due to its spectral correlations and spatial information abundant
The fields such as agricultural and mineral prospecting.Wherein, high-spectral data solution it is mixed be quantitative remote sensing analysis key technology.High-spectral data solution
Mixed basic principle is the combination by single pixel spectral resolution at several Pure pixel (end member) spectrum.Its theoretical foundation is
Due to the limitation of imaging spectrometer spatial resolution, there are a large amount of mixed pixel, each mixing in the high spectrum image of acquisition
It include a variety of pure substances (i.e. end member) in pixel.
Many solutions for high-spectral data have been proposed at present and mix algorithm, including Pure pixel index, vertex component
Analysis, independent component analysis and Related Component analysis etc..But the above mixed algorithm of solution is largely to be based on depositing in high-spectral data
In pure pixel it is assumed that practical high spectrum image is not fully consistent with this hypothesis.And the solution based on Non-negative Matrix Factorization is mixed
Model, which considers not only, does not include pure pixel in high spectrum image, and as it is assumed that and by being added to end member and abundance
Constraint, acquire optimal end member matrix and its corresponding abundance matrix.Miao and Qi proposes the constraint of end member minimum volume
Non-negative Matrix Factorization solution mix algorithm (MVCNMF) [Miao L., Qi H.Endmember extraction from highly
mixed data using minimum volume constrained nonnegative matrix factorization
[J] .IEEE Transactions on Geoscience andRemote Sensing, 2007,45 (3): 765-777.],
Qian etc. proposes abundance l1/2The Non-negative Matrix Factorization solution of sparsity constraints mixes algorithm (l1/2-NMF)[Qian Y.,Jia S.,
Zhou J.,Robles-KellyA.Hyperspectr--al unmixing vial1/2sparsity-constrained
Nonnegative Matrix Factorizat--ion[J].IEEE Transactions on Geoscience and
2011,49 (11): Remote Sensing 4282-4297.], achieves good solve and mixes effect.However, the above method is only
The correlation of EO-1 hyperion spectral information is utilized, without effective joint space-spectral information, it is lower to solve mixed precision, and when number
According to there are algorithm performances when noise to reduce.
Summary of the invention
Present invention aims at the EO-1 hyperion for fields such as atural object covering analyzing, precision agriculture and mineral investigation is unsupervised
Mixed problem is solved, proposes a kind of empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method.
The technical solution for realizing the aim of the invention is as follows: a kind of empty mixed side of spectrum joint multiconstraint optimization nonnegative matrix solution
Method includes the following steps:
Step 1, using the EO-1 hyperion signal subspace recognizer based on minimal error, estimate EO-1 hyperion end member quantity；
Step 2, minimum relationship, building endmember spectra minimum range constraint at a distance from geometry mass center based on endmember spectra
?；
Step 3, it based on the sparsity of abundance, constructs abundance and mixes norm sparsity constraints item；
Step 4, the characteristic based on high spectrum image Piecewise Smooth constructs abundance figure gradient field group's sparsity constraints item；
Step 5, by step 2,3,4 bound term and nonnegative matrix solution mix models coupling, it is excellent to establish empty spectrum joint multiple constraint
Change nonnegative matrix solution and mixes model；
Step 6, rule is updated according to alternating iteration, is two sub- optimization problems by model decomposition, and antithetical phrase optimization respectively
Problem is solved using change of direction multiplier method；
Step 7, output step 6 solves gained end member matrix and the corresponding abundance figure of each end member.
Further, step 1 EO-1 hyperion end member quantity survey detailed process are as follows:
(1) it handles original high-spectral data and obtains mode input
Original hyperspectral image data Y ∈ RL×W×H, wherein L indicates the wave band number of EO-1 hyperion, and W and H respectively indicate image
The width and height of Spatial Dimension；Original high-spectral data Y is scanned pixel-by-pixel and is sorted with column direction, spectrum matrix of picture elements is formed
X=[x1,x2,…,xi,…,xN]∈RL×N, wherein N=W × H indicates the number of EO-1 hyperion pixel, xi∈RL, indicate i-th of light
Compose pixel, 1≤i≤N；
(2) EO-1 hyperion end member quantity survey
Using the EO-1 hyperion signal subspace recognizer based on minimal error, the end member number of spectrum matrix of picture elements X is estimated
Amount is J.
Further, step 2 constructs endmember spectra minimum range bound term specifically:
Wherein, A=[a1,a2,…,aj,…,aJ]∈RL×JIndicate end member matrix, aj∈RLIndicate that j-th of end member, L indicate
The wave band number of EO-1 hyperion, J indicate the quantity of end member；1JIndicate the column vector that J value is 1.
Further, step 3 building abundance mixes norm sparsity constraints item specifically:
Wherein, S=[s1,s2,…,si,…,sN]∈RJ×NIndicate abundance matrix, si∈RJIndicate i-th of column vector of S, J
Indicate the quantity of end member, N indicates the pixel quantity in EO-1 hyperion；||·||1With | | | |2Respectively indicate l1Norm and l2Model
Number.
Further, step 4 building abundance figure gradient field group's sparsity constraints item specifically includes following 3 sub-steps:
Step 4-1: the horizontal difference of unknown abundance figure S is constructed, i.e.,
HhS=[d1,d2,…,dk,…,dn]
WhereinskWithIndicate that the abundance coefficient column vector an of pixel is horizontally adjacent with it
The abundance coefficient column vector of pixel；HhS∈RJ×N, Hh: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel horizontal direction difference；
Step 4-2: the vertical difference of unknown abundance figure S is constructed, i.e.,
HvS=[v1,v2,…,vk,…,vn]
WhereinskWithIndicate a pixel abundance coefficient column vector and it vertically adjacent to
The abundance coefficient column vector of pixel；HvS∈RJ×N, Hv: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel vertical direction difference；
Step 4-3: combined level difference and vertical difference construct the sparse item of gradient field group
Jtv(S)=| | HS | |1,1
Wherein,||·||1,1Indicate l1,1Norm.
Further, step 5 establishes empty spectrum joint multiconstraint optimization nonnegative matrix solution and mixes model specifically:
Wherein τA> 0, τS> 0, τtv> 0 is weight, X ∈ RL×NIt indicates wait solve mixed high-spectral data matrix, A ∈ RL ×JIndicate end member matrix, S ∈ RJ×NIndicate abundance matrix, | | | |FThe F norm of representing matrix,Indicate abundance matrix
The constraint of S abundance " and being one ",WithRespectively indicate the row vector that J value is 1 and the row vector that N number of value is 1.
Further, step 6 alternating direction iteratively solves detailed process are as follows:
(1) it is equivalence without constraint that the empty spectrum joint multiconstraint optimization nonnegative matrix solution for being established step 5, which mixes model conversion,
Optimal model:
Wherein lS() indicates the indicative function being defined on set S, as x ∈ S, lS(x)=0；WhenlS(x)=
∞, parameter δ > 0 controls the influence size of abundance " and being one " constraint；
(2) according to rule is alternately updated, the optimal model in (1) is decomposed into two sub- optimization problems:
Wherein, Sk+1Indicate the abundance matrix S, A in+1 iterative process of kthk+1Indicate the end in+1 iterative process of kth
Variable matrix A；
(3) S and A is iteratively solved
Random initializtion S first0With A0, then by S0With A0It brings the sub- optimization problem about S into, acquires the 1st iteration
S1, then by S1With A0It brings the sub- optimization problem about A into, acquires the A of the 1st iteration1, first time iteration terminates, and obtains S1With A1；
It is multiple to recycle above procedure, the iterative process of i-th are as follows:
By the S of the t-1 times iterationt-1With At-1Bring the sub- optimization problem about S into, the S of the t times iteration is acquired in t >=1t,
Again by StWith At-1It brings the sub- optimization problem about A into, acquires the A of the t times iterationt, the t times iteration terminates, and obtains StWith At；Repeatedly
For T times, until result restrains, to obtain final S and A.
Further, the mixed gained end member of step 7 output solution and abundance figure detailed process are as follows:
(1) output iteratively solves resulting end member matrix A and abundance matrix S；
(2) by abundance coefficient matrix S ∈ RJ×N, pixel-by-pixel according to original hyperspectral image data Y ∈ RL×W×HSpace dimension
Size is spent, three-dimensional matrice S '=[s ' is reassembled as1,…,s′j,…,s′J]∈RJ×W×H, s 'j∈RW×HIndicate j-th of end member in height
Abundance coefficient figure in spectroscopic data.
Compared with prior art, the present invention its distinguishing feature are as follows: (1) present invention has fully considered space in high spectrum image
With the characteristic of spectral information, frame is mixed in conjunction with nonnegative matrix solution, capable modeling is infiltrated to EO-1 hyperion sky-spectrum joint solution, it is non-with tradition
Negative matrix solution mixing method is compared, and is improved and is understood mixed precision, enhances algorithm noise robust；(2) it the composite can be widely applied to
The mixed application of the high-spectral data solution in the fields such as environmental monitoring, mineral exploration and precision agriculture.
Present invention is further described in detail with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method flow chart of the invention.
It is 20dB, 25dB, 30dB, the analogue data that 35dB, 40dB and noiseless lower wave band are 50 that Fig. 2, which is in noise intensity,
Schematic diagram.
Fig. 3 (a) is SAD index curve graph of the various algorithms under different noise intensities, and Fig. 3 (b) is various algorithms not
With the RMSE index curve graph under noise intensity.
Fig. 4 is the real data set Cuprite schematic diagram of the 50th wave band.
Fig. 5 (a) is empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method (SSCNMF) at simulated data sets SNR40
The curve of spectrum and real spectrum curve graph of 5 kinds of required end members, wherein abscissa indicates that wave band number, ordinate indicate reflection
Rate, dotted line are the curve of spectrum, and solid line is real spectrum curve；Fig. 5 (b) is that sparse constraint nonnegative matrix solution mixes algorithm (CSNMF)
The curve of spectrum and real spectrum curve graph of 5 kinds of required end members at simulated data sets SNR40, abscissa indicate wave band number,
Ordinate indicates that reflectivity, dotted line are the curve of spectrum, and solid line is real spectrum curve.
Fig. 6 (a)~Fig. 6 (e) is the corresponding true abundance figure of end member 1~5.
Fig. 7 (a)~Fig. 7 (e) is empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method (SSCNMF) in analogue data
Abundance figure corresponding to 5 kinds of end members required by collecting under SNR40, wherein Fig. 7 (a) is the corresponding abundance figure of end member 1, and Fig. 7 (b) is end
First 2 corresponding abundance figures, Fig. 7 (c) is the corresponding abundance figure of end member 3, and Fig. 7 (d) is the corresponding abundance figure of end member 4, and Fig. 7 (e) is
The corresponding abundance figure of end member 5.
Fig. 8 (a)~Fig. 8 (e) is that sparse constraint nonnegative matrix solution mixes algorithm (CSNMF) institute at simulated data sets SNR40
Abundance figure corresponding to the 5 kinds of end members asked, wherein Fig. 8 (a) is the corresponding abundance figure of end member 1, and Fig. 8 (b) is that end member 2 is corresponding rich
Degree figure, Fig. 8 (c) is the corresponding abundance figure of end member 3, and Fig. 8 (d) is the corresponding abundance figure of end member 4, and Fig. 8 (e) is that end member 5 is corresponding
Abundance figure.
Fig. 9 (a)~Fig. 9 (l) is that empty spectrum joint Non-negative Matrix Factorization solution mixes algorithm (SSCNMF) institute under real data set
The abundance figure for obtaining end member, respectively corresponds Alunite, Andradite, Buddingtonite, Dumortierite,
Kaolinite_1, Kaolinite_2, Muscovite, Montmorillonite, Nontronite, Pyrope, Sphene,
The abundance figure of this 12 kinds of mineral of Chalcedony.
Specific embodiment
In conjunction with Fig. 1, a kind of empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method includes the following steps:
Step 1, EO-1 hyperion end member quantity survey: by original EO-1 hyperion 3 d image data Y ∈ RL×W×H, scan pixel-by-pixel
It is sorted with column direction, is converted to two-dimension spectrum matrix of picture elements X=[x1,x2,…,xi,…,xN]∈RL×N, wherein L indicates bloom
The wave band number of spectrum, W and H respectively indicate the width and height of image space dimension, xi∈RL, N=W × H expression EO-1 hyperion pixel
Number.
Using the EO-1 hyperion signal subspace recognizer based on minimal error, the end member number of spectrum matrix of picture elements X is estimated
Amount is J.
Step 2, endmember spectra minimum range bound term is constructed:
Since EO-1 hyperion pixel is contained in a monomorphous in spectrum dimension, end member is the vertex of the monomorphous, and
The monomorphous has volume least commitment, i.e. monomorphous vertex is minimum to geometry centroid distance.It is tieed up by the above end member in spectrum
Geometrical property constructs endmember spectra minimum range bound term:
Wherein, A=[a1,a2,…,aj,…,aJ]∈RL×JIndicate end member matrix, aj∈RLIndicate that j-th of end member, L indicate
The wave band number of EO-1 hyperion, J indicate the quantity of end member；1JIndicate the column vector that J value is 1.
Step 3, building abundance mixes norm sparsity constraints item:
In most cases, the abundance distribution of any end member will not be throughout entire scene, each end member for high spectrum image
Abundance be it is local, that is, have a degree of sparsity, thus construct abundance mix norm sparsity constraints item:
Wherein, S=[s1,s2,…,si,…,sN]∈RJ×NIndicate abundance matrix, si∈RJIndicate i-th of column vector of S, J
Indicate the quantity of end member, N indicates the pixel quantity in EO-1 hyperion；||·||1With | | | |2Respectively indicate l1Norm and l2Model
Number.
Step 4, abundance figure gradient field group's sparsity constraints item is constructed:
Due to the continuity and homogeney of high spectrum image substance in spatial dimension, the i.e. continuity and homogeneity of abundance
Property, while can have the discontinuity of abundance mutation, belong to the information of EO-1 hyperion Spatial Dimension above, can be summarized as Piecewise Smooth
Property, abundance figure gradient field group's sparsity constraints item is thus constructed, specifically includes 3 sub-steps:
Step 4-1 constructs the horizontal difference of unknown abundance figure S, i.e.,
HhS=[d1,d2,…,dk,…,dn]
WhereinskWithIndicate that the abundance coefficient column vector an of pixel is horizontally adjacent with it
The abundance coefficient column vector of pixel；HhS∈RJ×N, Hh: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel horizontal direction difference；
Step 4-2: the vertical difference of unknown abundance figure S is constructed, i.e.,
HvS=[v1,v2,…,vk,…,vn]
WhereinskWithIndicate a pixel abundance coefficient column vector and it vertically adjacent to
The abundance coefficient column vector of pixel；HvS∈RJ×N, Hv: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel vertical direction difference；
Step 4-3, combined level difference and vertical difference construct the sparse item of gradient field group
Jtv(S)=| | HS | |1,1
Wherein,||·||1,1Indicate l1,1Norm, for example,Wherein xiFor X square
The i-th column vector in battle array.
Step 5, it establishes empty spectrum joint multiconstraint optimization nonnegative matrix solution and mixes model:
Wherein τA> 0, τs> 0, τtv> 0, X ∈ RL×NIt indicates wait solve mixed high-spectral data matrix, A ∈ RL×JIndicate end member
Matrix, S ∈ RJ×NIndicate abundance matrix, | | | |FThe F norm of representing matrix,Expression S abundance matrix abundance " and be
One " constraint,WithRespectively indicate the row vector that J value is 1 and the row vector that N number of value is 1.
Step 6, alternating direction iteratively solves:
(1) it is equivalence without constraint that the empty spectrum joint multiconstraint optimization nonnegative matrix solution for being established step 5, which mixes model conversion,
Optimal model:
Wherein lS() indicates the indicative function being defined on set S (as x ∈ S, lS(x)=0；WhenlS(x)=
∞), parameter δ > 0 controls the influence size of abundance " and being one " constraint.
(2) according to rule is alternately updated, the optimal model in (1) is decomposed into two sub- optimization problems:
Wherein, Sk+1Indicate the abundance matrix S, A in+1 iterative process of kthk+1Indicate the end in+1 iterative process of kth
Variable matrix A.
(3) S and A is iteratively solved
Random initializtion S first0With A0, then by S0With A0It brings the sub- optimization problem about S into, acquires the 1st iteration
S1, then by S1With A0It brings the sub- optimization problem about A into, acquires the A of the 1st iteration1, first time iteration terminates, and obtains S1With A1。
It is multiple to recycle above procedure, the iterative process of i-th are as follows:
By the S of the t-1 times iterationt-1With At-1Bring the sub- optimization problem about S into, the S of the t times iteration is acquired in t >=1t,
Again by StWith At-1It brings the sub- optimization problem about A into, acquires the A of the t times iterationt, the t times iteration terminates, and obtains StWith At；Repeatedly
For T times, until result restrains, to obtain final S and A.
Step 7, the mixed gained end member of output solution and abundance figure:
(1) output iteratively solves resulting end member matrix A and abundance matrix S.
(2) by abundance coefficient matrix S ∈ RJ×N, pixel-by-pixel according to original hyperspectral image data Y ∈ RL×W×HSpace dimension
Size is spent, three-dimensional matrice S '=[s ' is reassembled as1,…,s′j,…,s′J]∈RJ×W×H, s 'j∈RW×HIndicate j-th of end member in height
Abundance coefficient figure in spectroscopic data.
The present invention makes full use of the geometrical property of high optical spectrum image end member spectrum dimension space, abundance sparse characteristic and abundance figure
The Piecewise Smooth characteristic in Spatial Dimension；It is used as bound term that nonnegative matrix solution is added simultaneously extracted spectrum and spatial information
Mixed model.Multiple constraint method can prevent from falling into local minimum solution, and optimal solution can be obtained.This method and traditional classical nonnegative matrix solution
Mixed model method is compared, and is improved and is understood mixed precision, while enhancing the robustness to noise.
The present invention is described in detail with reference to the accompanying drawings and examples.
Embodiment
In conjunction with Fig. 1, a kind of empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method, steps are as follows:
The first step, EO-1 hyperion end member quantity survey
(1) it handles original high-spectral data and obtains mode input
Original hyperspectral image data Y ∈ RL×W×H, wherein L indicates the wave band number of EO-1 hyperion, and W and H respectively indicate image
The width and height of Spatial Dimension.Original high-spectral data Y is scanned into the column direction row with Spatial Dimension row, column direction pixel-by-pixel
Sequence forms spectrum matrix of picture elements X=[x1,x2,…,xi,…,xN]∈RL×N, wherein N=W × H indicates of EO-1 hyperion pixel
Number, xi∈RL, indicate i-th of spectrum pixel, 1≤i≤N.
(2) EO-1 hyperion end member quantity survey
Using the EO-1 hyperion signal subspace recognizer based on minimal error, the end member number of spectrum matrix of picture elements X is estimated
Amount is J.
Second step constructs endmember spectra minimum range bound term
Wherein, A=[a1,a2,…,aj,…,aJ]∈RL×JIndicate end member matrix, aj∈RLIndicate that j-th of end member, L indicate
The wave band number of EO-1 hyperion, J indicate the quantity of end member；1JIndicate the column vector that J value is 1.
Third step, building abundance mix norm sparsity constraints item
Wherein, S=[s1,s2,…,si,…,sN]∈RJ×NIndicate abundance matrix, si∈RJIndicate i-th of column vector of S, J
Indicate the quantity of end member, N indicates the pixel quantity in EO-1 hyperion；||·||1With | | | |2Respectively indicate l1Norm and l2Model
Number.
4th step constructs abundance figure gradient field group's sparsity constraints item
This step specifically includes 3 sub-steps:
Step 4-1: the horizontal difference of unknown abundance figure S is constructed, i.e.,
HhS=[d1,d2,…,dk,…,dn]
WhereinskWithIndicate that the abundance coefficient column vector an of pixel is horizontally adjacent with it
The abundance coefficient column vector of pixel；HhS∈RJ×N, Hh: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel horizontal direction difference；
Step 4-2: the vertical difference of unknown abundance figure S is constructed, i.e.,
HvS=[v1,v2,…,vk,…,vn]
WhereinskWithIndicate a pixel abundance coefficient column vector and it vertically adjacent to
The abundance coefficient column vector of pixel；HvS∈RJ×N, Hv: RJ×n→RJ×nA linear operator is indicated, for calculating in S Spatial Dimension
Adjacent pixel vertical direction difference；
Step 4-3: combined level difference and vertical difference construct the sparse item of gradient field group
Jtv(S)=| | HS | |1,1
Wherein,||·||1,1Indicate l1,1Norm, for example,Wherein xiFor X square
The i-th column vector in battle array.
5th step establishes empty spectrum joint multiconstraint optimization nonnegative matrix solution and mixes model
Wherein τA> 0, τS> 0, τtv> 0, τAValue range be { 0.5,5,50 }, τSValue range be { 5e-3,5e-
2,5e-1 }, τtvValue range be { 5e-3,5e-2,5e-1 }, X ∈ RL×NIt indicates wait solve mixed high-spectral data matrix, A ∈ RL ×JIndicate end member matrix, S ∈ RJ×NIndicate abundance matrix, | | | |FThe F norm of representing matrix,Indicate S abundance square
The constraint of battle array abundance " and being one ",WithRespectively indicate the row vector that J value is 1 and the row vector that N number of value is 1.
6th step, alternating direction iterative solution
(1) it is of equal value without constraining most that the empty spectrum joint multiconstraint optimization nonnegative matrix solution for establishing the 5th step, which mixes model conversion,
Optimized model:
Wherein lS() indicates the indicative function being defined on set S (as x ∈ S, lS(x)=0；Whenls(x)=
∞), parameter δ > 0 controls the influence size of abundance " and being one " constraint, and the value range of δ is { 0.5,1,5,10 }.
(2) according to rule is alternately updated, the optimal model in (1) is decomposed into two sub- optimization problems:
Wherein, Sk+1Indicate the abundance matrix S, A in+1 iterative process of kthk+1Indicate the end in+1 iterative process of kth
Variable matrix A.
(3) S and A is iteratively solved
Random initializtion S first0With A0, then by S0With A0It brings the sub- optimization problem about S into, acquires the 1st iteration
S1, then by S1With A0It brings the sub- optimization problem about A into, acquires the A of the 1st iteration1, first time iteration terminates, and obtains S1With A1。
It is multiple to recycle above procedure, the iterative process of i-th are as follows:
By the S of the t-1 times iterationt-1With At-1Bring the sub- optimization problem about S into, the S of the t times iteration is acquired in t >=1t,
Again by StWith At-1It brings the sub- optimization problem about A into, acquires the A of the t times iterationt, the t times iteration terminates, and obtains StWith At；Repeatedly
For T times, until result restrains, to obtain final S and A, the value range of T is { 300,500,1000 }.
7th step, output solve mixed result
(1) output iteratively solves resulting end member matrix A and abundance matrix S.
(2) by abundance coefficient matrix S ∈ RJ×N, pixel-by-pixel according to original hyperspectral image data Y ∈ RL×W×HSpace dimension
Size is spent, three-dimensional matrice S '=[s ' is reassembled as1,…,s′j,…,s′J]∈RJ×W×H, s 'h∈RW×HIndicate j-th of end member in height
Abundance coefficient figure in spectroscopic data.
Effect of the invention can be further illustrated by following emulation experiment:
(1) simulated conditions
Emulation experiment is using simulation high-spectral data and two data of real data collection: (1) analogue data generates 75 × 75
A pixel, each pixel has 224 wave bands, as shown in Fig. 2, Fig. 2 is illustrated under different noise intensities, the mould of the 50th wave band
Quasi- data image, the high, wide of image is respectively 75 pixels, 75 pixels.Simulated data sets are raw using linear mixed model
At: end member of 5 spectral modeling SAD greater than 4.44 is randomly selected from USGS end member library first, forms end member matrix；Then it generates
The corresponding abundance figure of each end member, and abundance " and being one " (ASC, abundance sum-to- is added in abundance matrix
One constraint) constraint；End member matrix is mixed using linear mixed model with abundance matrix finally, and Gauss zero is added
For mean value white noise as error, noise intensity is respectively 20dB, 25dB, 30dB, 35dB, 40dB with it is noiseless, obtain six groups of moulds
Quasi- data.(2) practical high-spectral data collection is well-known aviation visible light/infrared thermoviewer (Visible InfraRed
Imaging Spectrometer, AVIRIS) shooting Cuprite data set.Data used in experiment are Cuprite data
A part, it includes 224 wave bands between 400 to 2500 nanometers, spectrum point that Spatial Dimension size, which is 250 × 191 pixels,
Resolution is 10 nanometers.Before carrying out this experiment, wave band 1-2,105-115,150-170,223-224 due to water vapor absorption and
The larger reason of noise is removed, remaining 188 available bands.Fig. 4 is the space of the 50th wave band in real data set Cuprite
Image, Gao Yukuan are respectively 250 pixels, 191 pixels.
Emulation experiment is completed under 7 operating system of Windows using MATLAB R2016a.
(2) emulation content
The present invention mixes effect using the solution of simulation high-spectral data collection and true high-spectral data collection check algorithm.For test
The performance of inventive algorithm, by empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method (SSCNMF) of proposition and the current world
The nonnegative matrix solution of upper prevalence mixes algorithm comparison.Control methods includes: that the Non-negative Matrix Factorization solution of minimum volume constraint mixes algorithm
(MVCNMF), the Non-negative Matrix Factorization solution of minimum range constraint mixes algorithm (MDCNMF) [Yu Y., Guo S., Sun
W.Minimum distance constrained non-negative matrix factorization for the
endmember extraction of hyperspectral images[C].Proceedings ofthe SPIE,2007:
6790151-6790159.], l1/2The Non-negative Matrix Factorization solution of sparsity constraints mixes algorithm (l1/2- NMF), it is based on l1-l2Sparsity
The Non-negative Matrix Factorization solution of measurement constraint mixes algorithm (CSNMF) [Liu J, Wu Z, Wei Z, et al.A novel sparsity
constrained nonnegative matrix factorization for hyperspectral unmixing[C]//
Geoscience and Remote Sensing Symposium.IEEE,2012:1389-1392.]。
The evaluation index that the present invention uses is that spectrum angular distance (SAD, SpectralAngle Distance) and root are equal
Square error (RMSE, RootMean Square Error).
(3) the simulation experiment result is analyzed
(1) simulated data sets
It can be seen that by Fig. 3 (a) and Fig. 3 (b), the present invention under multiple noise intensities, has smaller compared to other algorithms
SAD and RSME.It can be seen that from Fig. 5 (a) and Fig. 5 (b), Fig. 5 (a) and real spectrum curve are more identical, and by calculating Fig. 5
(a) the spectral modeling SAD, Fig. 5 (a) with the end member curve of spectrum in Fig. 5 (b) and actual spectrum have smaller sad value.By Fig. 6, Fig. 7
It is compared with Fig. 8, the solution mixing method proposed by the present invention for merging Piecewise Smooth spatial information it can be seen from Fig. 7 (a)-(e)
Gained abundance figure is closer to the true abundance figure of Fig. 6 (a)-(e).Therefore, SSCNMF ratio CSNMF of the present invention has higher solution mixed
Precision.
(2) real data collection
Table 1 shows that real data collection by the sad value of 12 kinds of end members and true end member obtained by many algorithms, passes through comparison
It was found that end member SAD mean value obtained by SSCNMF is minimum.Fig. 9 show 12 kinds of end members obtained by SSCNMF of the present invention it is corresponding 12 it is rich
Degree figure.
Table 1
| MVC | MDC | L1/2 | CSNMF | SSCNMF | |
| #1Alunite | 0.1511 | 0.1642 | 0.122 | 0.2226 | 0.2332 |
| #2Andradite | 0.3785 | 0.3124 | 0.2878 | 0.1911 | 0.0725 |
| #3Buddingtonite | 0.8454 | 0.1358 | 0.1101 | 0.255 | 0.1145 |
| #4Dumortierite | 0.2446 | 0.2899 | 0.1369 | 0.091 | 0.2157 |
| #5Kaolinite_1 | 0.1519 | 0.2023 | 0.111 | 0.1228 | 0.1924 |
| #6Kaolinite_2 | 0.1569 | 0.2482 | 0.2477 | 0.0718 | 0.0604 |
| #7Muscovite | 0.0956 | 0.0899 | 0.446 | 0.4054 | 0.3186 |
| #8Montmorillonite | 0.2689 | 0.4151 | 0.0716 | 0.0814 | 0.0683 |
| #9Nontronite | 0.2033 | 0.2136 | 0.1185 | 0.0908 | 0.0981 |
| #10Pyrope | 0.0852 | 0.1916 | 0.1911 | 0.0633 | 0.0613 |
| #11Sphene | 0.2438 | 0.283 | 0.1378 | 0.0544 | 0.1368 |
| #12Chalcedony | 0.3386 | 0.3391 | 0.0934 | 0.0997 | 0.0923 |
| Average | 0.26366 | 0.24041 | 0.17282 | 0.14578 | 0.13868 |
Two above the experimental results showed that, the method for the present invention passes through that Piecewise Smooth is incorporated in Non-negative Matrix Factorization solution is mixed is empty
Between information it is mixed to carry out empty spectrum information joint multiconstraint optimization solution, can get it is higher solve mixed precision, obtain preferably solving mixed effect
Fruit, and have stronger noise robust.
Claims (8)
1. a kind of empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method, which comprises the steps of:
Step 1, using the EO-1 hyperion signal subspace recognizer based on minimal error, estimate EO-1 hyperion end member quantity；
Step 2, based on endmember spectra at a distance from geometry mass center minimum relationship, construct endmember spectra minimum range bound term；
Step 3, it based on the sparsity of abundance, constructs abundance and mixes norm sparsity constraints item；
Step 4, the characteristic based on high spectrum image Piecewise Smooth constructs abundance figure gradient field group's sparsity constraints item；
Step 5, by step 2,3,4 bound term and nonnegative matrix solution mix models coupling, it is non-to establish empty spectrum joint multiconstraint optimization
Negative matrix solution mixes model；
Step 6, rule is updated according to alternating iteration, is two sub- optimization problems by model decomposition, and respectively to sub- optimization problem
It is solved using change of direction multiplier method；
Step 7, output step 6 solves gained end member matrix and the corresponding abundance figure of each end member.
2. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 1, which is characterized in that step 1
EO-1 hyperion end member quantity survey detailed process are as follows:
(1) it handles original high-spectral data and obtains mode input
Original hyperspectral image data Y ∈ RL×W×H, wherein L indicates the wave band number of EO-1 hyperion, and W and H respectively indicate image space
The width and height of dimension；Original high-spectral data Y is scanned pixel-by-pixel and is sorted with column direction, spectrum matrix of picture elements X=is formed
[x1,x2,…,xi,…,xN]∈RL×N, wherein N=W × H indicates the number of EO-1 hyperion pixel, xi∈RL, indicate i-th of spectral image
Member, 1≤i≤N；
(2) EO-1 hyperion end member quantity survey
Using the EO-1 hyperion signal subspace recognizer based on minimal error, estimate that the end member quantity of spectrum matrix of picture elements X is J
It is a.
3. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 2, which is characterized in that step 2
Construct endmember spectra minimum range bound term specifically:
Wherein, A=[a1,a2,…,aj,…,aJ]∈RL×JIndicate end member matrix, aj∈RLIndicate that j-th of end member, L indicate bloom
The wave band number of spectrum, J indicate the quantity of end member；1JIndicate the column vector that J value is 1.
4. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 3, which is characterized in that step 3
It constructs abundance and mixes norm sparsity constraints item specifically:
Wherein, S=[s1,s2,…,si,…,sN]∈RJ×NIndicate abundance matrix, si∈RJIndicate i-th of column vector of S, J is indicated
The quantity of end member, N indicate the pixel quantity in EO-1 hyperion；||·||1With | | | |2Respectively indicate l1Norm and l2Norm.
5. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 4, which is characterized in that step 4
Constructing abundance figure gradient field group's sparsity constraints item specifically includes following 3 sub-steps:
Step 4-1: the horizontal difference of unknown abundance figure S is constructed, i.e.,
HhS=[d1,d2,…,dk,…,dn]
WhereinskWithIndicate the abundance coefficient column vector and its horizontally adjacent pixel of a pixel
Abundance coefficient column vector；HhS∈RJ×N, Hh: RJ×n→RJ×nIndicate a linear operator, it is adjacent in S Spatial Dimension for calculating
Pixel level direction difference；
Step 4-2: the vertical difference of unknown abundance figure S is constructed, i.e.,
HvS=[v1,v2,…,vk,…,vn]
WhereinskWithIndicate a pixel abundance coefficient column vector and it vertically adjacent to pixel
Abundance coefficient column vector；HvS∈RJ×N, Hv: RJ×n→RJ×nIndicate a linear operator, it is adjacent in S Spatial Dimension for calculating
Pixel vertical direction difference；
Step 4-3: combined level difference and vertical difference construct the sparse item of gradient field group
Jtv(S)=| | HS | |1,1
Wherein,||·||1,1Indicate l1,1Norm.
6. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 5, which is characterized in that step 5
It establishes empty spectrum joint multiconstraint optimization nonnegative matrix solution and mixes model specifically:
Wherein τA> 0, τS> 0, τtv> 0 is weight, X ∈ RL×NIt indicates wait solve mixed high-spectral data matrix, A ∈ RL×JTable
Show end member matrix, S ∈ RJ×NIndicate abundance matrix, | | | |FThe F norm of representing matrix,Indicate that abundance matrix S is rich
The constraint of degree " and being one ",WithRespectively indicate the row vector that J value is 1 and the row vector that N number of value is 1.
7. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 6, which is characterized in that step 6
Alternating direction iteratively solves detailed process are as follows:
(1) it is equivalence without constrained optimum that the empty spectrum joint multiconstraint optimization nonnegative matrix solution for being established step 5, which mixes model conversion,
Change model:
Wherein ls() indicates the indicative function being defined on set S, as x ∈ S, lS(x)=0；WhenlS(x)=∞, ginseng
Number δ > 0 controls the influence size of abundance " and being one " constraint；
(2) according to rule is alternately updated, the optimal model in (1) is decomposed into two sub- optimization problems:
Wherein, Sk+1Indicate the abundance matrix S, A in+1 iterative process of kthk+1Indicate the end member square in+1 iterative process of kth
Battle array A；
(3) S and A is iteratively solved
Random initializtion S first0With A0, then by S0With A0It brings the sub- optimization problem about S into, acquires the S of the 1st iteration1, then
By S1With A0It brings the sub- optimization problem about A into, acquires the A of the 1st iteration1, first time iteration terminates, and obtains S1With A1；Circulation
Above procedure is multiple, the t times iterative process are as follows:
By the S of the t-1 times iterationt-1With At-1Bring the sub- optimization problem about S into, the S of the t times iteration is acquired in t >=1t, then by St
With At-1It brings the sub- optimization problem about A into, acquires the A of the t times iterationt, the t times iteration terminates, and obtains StWith At；Iteration T times,
Until result restrains, to obtain final S and A.
8. empty spectrum joint multiconstraint optimization nonnegative matrix solution mixing method according to claim 7, which is characterized in that step 7
The mixed gained end member of output solution and abundance figure detailed process are as follows:
(1) output iteratively solves resulting end member matrix A and abundance matrix S；
(2) by abundance coefficient matrix S ∈ RJ×N, pixel-by-pixel according to original hyperspectral image data Y ∈ RL×W×HSpatial Dimension it is big
It is small, it is reassembled as three-dimensional matrice S '=[s '1,…,s′j,…,s′J]∈RJ×W×H, s 'j∈RW×HIndicate j-th of end member in EO-1 hyperion
Abundance coefficient figure in data.
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110428454A (en) * | 2019-08-13 | 2019-11-08 | 电子科技大学中山学院 | Hyperspectral unmixing method and device, electronic equipment and storage medium |
| CN110428369A (en) * | 2019-06-20 | 2019-11-08 | 中国地质大学（武汉） | CHNMF remote sensing images solution based on comentropy mixes algorithm |
| CN110610508A (en) * | 2019-08-20 | 2019-12-24 | 全球能源互联网研究院有限公司 | Static video analysis method and system |
| CN111260576A (en) * | 2020-01-14 | 2020-06-09 | 哈尔滨工业大学 | Hyperspectral unmixing algorithm based on de-noising three-dimensional convolution self-coding network |
| CN111508065A (en) * | 2020-04-15 | 2020-08-07 | 铜陵学院 | Hyperspectral reconstruction method, device and system based on space-spectrum joint compressed sensing |
| CN111914893A (en) * | 2020-06-24 | 2020-11-10 | 西安交通大学 | Hyperspectral unmixing method and system based on entropy regular nonnegative matrix decomposition model |
| CN112036235A (en) * | 2020-07-17 | 2020-12-04 | 中国科学院空天信息创新研究院 | Hyperspectral image target detection method and system |
| CN113094645A (en) * | 2021-03-11 | 2021-07-09 | 南京理工大学 | Hyperspectral data unmixing method based on morphological component constraint optimization |
| CN115272873A (en) * | 2022-09-27 | 2022-11-01 | 山东大学 | Hyperspectral image nonlinear feature preprocessing system and method based on gradient domain |
| CN115829886A (en) * | 2022-12-21 | 2023-03-21 | 哈尔滨师范大学 | Blind hyperspectral unmixing method based on end member self-adaptive incoherence and space constraint |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104899850A (en) * | 2014-03-03 | 2015-09-09 | 五邑大学 | High-spectrum image unmixing method based on weighted joint sparse regression |
| CN104952050A (en) * | 2015-07-07 | 2015-09-30 | 西安电子科技大学 | Self-adaptive hyperspectral image unmixing method based on region segmentation |
| CN105809105A (en) * | 2016-02-06 | 2016-07-27 | 黑龙江科技大学 | High-spectrum image demixing method based on end-member constraint non-negative matrix decomposition |
| US20160358335A1 (en) * | 2014-02-21 | 2016-12-08 | Ventana Medical Systems, Inc. | Group sparsity model for image unmixing |
-
2018
- 2018-08-02 CN CN201810871705.9A patent/CN109241843B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20160358335A1 (en) * | 2014-02-21 | 2016-12-08 | Ventana Medical Systems, Inc. | Group sparsity model for image unmixing |
| CN104899850A (en) * | 2014-03-03 | 2015-09-09 | 五邑大学 | High-spectrum image unmixing method based on weighted joint sparse regression |
| CN104952050A (en) * | 2015-07-07 | 2015-09-30 | 西安电子科技大学 | Self-adaptive hyperspectral image unmixing method based on region segmentation |
| CN105809105A (en) * | 2016-02-06 | 2016-07-27 | 黑龙江科技大学 | High-spectrum image demixing method based on end-member constraint non-negative matrix decomposition |
Non-Patent Citations (2)
| Title |
|---|
| JIANJUN LIU等: "A NOVEL SPARSITY CONSTRAINED NONNEGATIVE MATRIX FACTORIZATION FOR HYPERSPECTRAL UNMIXING", 《2012 IEEE INTERNATIONAL GEOSCIENCE AND REMOTE SENSING SYMPOSIUM》 * |
| YUNTAO QIAN等: "Hyperspectral Unmixing via L1/2 Sparsity-Constrained Nonnegative Matrix Factorization", 《IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING》 * |
Cited By (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110428369B (en) * | 2019-06-20 | 2021-10-08 | 中国地质大学（武汉） | CHNMF remote sensing image unmixing method based on information entropy |
| CN110428369A (en) * | 2019-06-20 | 2019-11-08 | 中国地质大学（武汉） | CHNMF remote sensing images solution based on comentropy mixes algorithm |
| CN110428454A (en) * | 2019-08-13 | 2019-11-08 | 电子科技大学中山学院 | Hyperspectral unmixing method and device, electronic equipment and storage medium |
| CN110610508A (en) * | 2019-08-20 | 2019-12-24 | 全球能源互联网研究院有限公司 | Static video analysis method and system |
| CN111260576B (en) * | 2020-01-14 | 2022-07-05 | 哈尔滨工业大学 | Hyperspectral unmixing algorithm based on de-noising three-dimensional convolution self-coding network |
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| CN111508065A (en) * | 2020-04-15 | 2020-08-07 | 铜陵学院 | Hyperspectral reconstruction method, device and system based on space-spectrum joint compressed sensing |
| CN111914893A (en) * | 2020-06-24 | 2020-11-10 | 西安交通大学 | Hyperspectral unmixing method and system based on entropy regular nonnegative matrix decomposition model |
| CN111914893B (en) * | 2020-06-24 | 2023-09-12 | 西安交通大学 | Hyperspectral unmixing method and hyperspectral unmixing system based on entropy regular non-negative matrix factorization model |
| CN112036235A (en) * | 2020-07-17 | 2020-12-04 | 中国科学院空天信息创新研究院 | Hyperspectral image target detection method and system |
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